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on both curves :

X(3), X(6), X(25)

vertices of the tangential triangle

on K1054a :

X(3129), X(3438), X(3440), X(3490), X(11142), X(11243), X(19305)

on K1054b :

X(3130), X(3439), X(3441), X(3489), X(11141), X(11244), X(19304)

Geometric properties :

K1054a = pK(X32, X3129) and K1054b = pK(X32, X3130) are the isogonal transforms of K1053a and K1053b respectively hence they are both anharmonically equivalent to the Neuberg cubic K001. See Table 20.

K1054a and K1054b are two members of the pencil of pKs with pole X(32) and pivots on the Euler line generated by K172 and K108, the isogonal transforms of the Lucas cubic K007 and the Droussent cubic K008 respectively.